Software localization

The software is recently localized into following languages:

English

Slovak

Software compatibility

The software has been created in MATLAB-Simulink programming environment and uses its graphical user interface to make software more interactive. Therefore it can be run in MATLAB v7 - Simulink v6.5 and newer.

Software installation

To install the software in a successful way, go through the following seven steps:

Step Response Data

Two windows are opened. First one contains figure with step response of output variable y(t) and control input u(t). The second one contains a table where the user must enter parameters of the identified process.

t_1 – the time corresponding to the tangent step response inflex point in the parameter y_0

t_2 –the time corresponding to the tangent step response inflex point in the parameter y_Inf

Sim_Time – simulation time

When all parameters are specified, use button [Identification]. The new window with 2 options of step response types is opened:

1st Order System

n – th Order System

Using the button [1st Order System], the software makes the identification by the Strejc method to obtain aperiodic model by approximation by 1st order system.

Using the button [n-th Order System], the software makes the identification by the Strejc method to obtain the aperiodic model, but this model cannot be described by 1st order transfer function.

Then 3 windows are opened:

First one contains figure with step response of output variable y(t) and the tangent line.

The second one contains parameters of identified process and button [Controller Tuning]. Using this button process of controller tuning will start (see the section "Controller Tuning")

Third one contains 3 other options:

Identification Tuning – you can receive the transfer function, which generates the step response that covers the original one more precisely. The difference between the original step response and the step response obtained by the identification using the modified position of the tangent is directly displayed as a red area in the new window.

Comparison – software compares the original and identified step response graphically and analytically.

Get lower order model – you can receive the transfer function of the system by approximation of identified model by lower order model.

When all parameters are specified, use button [Identification]. Then 3 windows are opened:

First one contains figure with step response of output variable y(t).

The second one contains parameters of identified process and button [Controller Tuning]. By using this button process of controller tuning will start (see the section "Controller Tuning").

Third one contains 2 other options:

Identification Tuning – you can receive the transfer function, which generates the step response that covers the original one more precisely. The difference between the original step response and the step response obtained by the identification using the modified position of the tangent is directly displayed as a red area in the new window.

Comparison – software compares the original and identified step response graphically and analytically.

Nonminimal phase

You must enter input parameters:

u_0 – initial value of the input variable u(t)

u_Inf – final value of input variable u(t)

t_0 – the time of step response

t_D – the time of the change of the output variable i.e. time delay

y_0 – initial value of output variable y(t)

t_Min – time which corresponds to y_Min

y_Min - minimum value of the output when the gain is greater than 0 (or the maximum, if gain is less than 0)

When all parameters are specified, use button [Identification]. Then 3 windows are opened:

First one contains figure with step response of output variable y(t).

The second one contains parameters of identified process and button [Controller Tuning]. Using this button process of controller tuning will start (see the section "Controller Tuning") Third one contains 3 other options:

Identification Tuning – you can receive the transfer function, which generates the step response that covers the original one more precisely. The difference between the original step response and the step response obtained by the identification using the modified position of the tangent is directly displayed as a red area in the new window.

Comparison – software compares the original and identified step response graphically and analytically.

Get lower order model – you can receive the transfer function of the system by approximation of identified model by lower order model (lower than 1 does not exist)

1st or 2nd Order System

You must enter input parameters:

n – system order (possibility to choose the 1st or the 2nd order system)

u_0 – initial value of the input variable u(t)

u_Inf – final value of input variable u(t)

t_0 – the time of step response

t_D – the time of the change of the output variable i.e. time delay

y_0 – initial steady-state value of the output variable

t_33 – time which corresponds to the value of output of 33% gain

t_70 - time which corresponds to the value of output of 70% gain

y_Inf – final value of output variable y(t)

Sim_Time – simulation time

When all parameters are specified, use button [Identification]. Then 3 windows are opened:

First one contains figure with step response of output variable y(t).

The second one contains parameters of identified process and button [Controller Tuning]. Using this button process of controller tuning will start (see the section "Controller Tuning").

Third one contains 3 other options:

Identification Tuning – you can receive the transfer function, which generates the step response that covers the original one more precisely. The difference between the original step response and the step response obtained by the identification using the modified position of the tangent is directly displayed as a red area in the new window.

Comparison – software compares the original and identified step response graphically and analytically.

Get lower order model – you can receive the transfer function of the system by approximation of identified model by lower order model (lower than 1 does not exist).

Load the Data File

The program opens the new window, where the user can comfortably find out a required data file containing recorded step-response data. The considered structure of the data file is as follows, the first column vector represents a time and the second column vector represents associated measured values of the output variable.

Next window shows a figure of the step response. Another window requires entering the parameter for normalization:

t_0 – the time of the step change

delta_u – size of the step change

Use the button [Normalization]. Next window shows a figure of normalized step response.

In the next window, there is a choice of data processing:

Filtration

Identification

To obtain the aperiodic model of the controlled process, the user can directly use the button [Identification]. When the damped periodic model is required, the user can simply activate the checkbox [Periodic process] and then use the button [Identification]. If the controlled process has been identified using the Strejc method, the tangent to the step response is also depicted and its equation is given.

Filtration

If the loaded step–response data are noisy, the user can use the filtration before identification, simply using the button [Filtration]. Then the new window for filtration is opened. You must enter input parameters:

order – order of the filter n

omega – filter frequency (values from [0;1])

User gets:

Filtration error – difference between filtered signal and origin

All entered parameters are needed to count parameters of the filter a, b. These coefficients can be counted by using different methods. It is possible to design non-recursive filter parameters (FIR).
Types of the recursive filter (IIR):

Butterworth

Chebyshev

Chebyshev inv.

elliptical

With regard to the frequency of affecting the measured signal can be selected from various types of the proposed filter:

low-pass

high-pass

bandstop

There is a choice of the method of filtration:

simple

improved

After filtration software automatically displays a graph of filtered and unfiltered signal for easier visual evaluation of filtration.

By using the button [Save], the user can simply store reached filtered data into the new data file for later usage. After filtration, identification can be started.

Process Model Data

The program opens a new window for the transfer function of the known parameters of the model. User can choose type of the transfer function

General transfer function

Aperiodic

Damped Periodic

General transfer function

You must enter input parameters:

NUM - numerator of the model system transfer function

DEN - denominator of the model system transfer function

D – time delay

Sim_Time – simulation time

To obtain the aperiodic model of the controlled process, the user can directly use the button Identification. When the damped periodic model is required, the user can simply activate the checkbox [Periodic process] and then use the button [Identification].

Results of the identification will be displayed in new windows.

Aperiodic

You must enter input parameters:

n - order

K - gain

T - time constant

Sim_Time – simulation time

Software makes the identification by the Strejc method to obtain aperiodic model by approximation using the lower order system if required.
Results of the identification will be displayed in new windows

Damped Periodic

You must enter input parameters:

K - gain

T_pe - time constant

ksi_pe - damping coefficient - values from an interval [0;1]

D_pe - time delay

Sim_Time - simulation time

Results of the identification will be displayed in new windows.

Controller Tuning

Using the button [Controller Tuning] of the main window, the new window for controlled system parameters design will be opened.

Choose a type of the system on the upper side of the window. There are two options:

Transfer function by Strejc The aperiodic process can be described using transfer function by Strejc in (1)

G = K/(Ts + 1)^nexp( - D*s) (1)

Inputs of the transfer function by Strejc:

n - order

K - gain

T - time constant

D - time delay

Damped periodic transfer function

The damped periodic process can be described using the associated parameters of the transfer function in (2).

G_pe = K/(T_pe^2s + 2ksi_peT_pes + 1)exp( - D_pes) (2)

Inputs of the damped periodic transfer function:

K - gain

T_pe - time constant

ksi_pe - damping coefficient - values are an open interval (0;1)

D_pe - time delay

Using the button [Controller Tuning] opens the new window for PID controller tuning. The required type of the PID controller can be chosen using the associated radio-button:

P

PI

PID

PD

and choosing the radio-button of the required class of controller tuning methods:

Experimental methods

Analytical methods

Using the popup menu enables to choose from the list of the available methods.

Using the button [Controller tuning] the controller with the set properties will be designed. A new window for control performance check using the simulation of control will be opened.

PID Controller Parameters

In the upper left part of the window are shown the calculated parameters of the designed controller in (3)

Gr = (Z_Rs + Z_R/T_I + Z_RT_D*s^2)/s (3)

Input & Output parameters:

Z_R - proportional gain

T_I - integral time constant

T_D - derivative time constant

T_R – anti-windup gain parameter of an integral part

T_D - filter of the derivative part

Process Model

In the upper right part are shown the parameters of the controlled system in (4)

G = NUM/DENexp( - Ds) (4)

Input & Output parameters:

NUM - numerator of the controlled system transfer function

DEN - denominator of the controlled system transfer function

D - time delay of the controlled system

Setpoint w(t)

In the middle left part of are shown the parameters for the setpoint tracking. Input parameters:

W_Initial - initial value of set point

W_Final - final value of set point

W_Step_Change - time of the step change

Disturbance r(t)

In the middle right part of are shown the parameters for the disturbance rejection.

Input parameters:

R_Initial - initial value of disturbance

R_Final - final value of disturbance

R_Step_Change - time of the step change

Simulation parameters

In the upper right part are shown simulation parameters Input parameters:

Control_Precision - tolerance of the setpoint neighborhood

Sim_Time - simulation time

U_Min_Boundary - lower constraint on the control input

U_Max_Boundary - upper constraint on the control input

Using the button [Step response] the simulation of control will be started.

Then the various figures are opened:

poles and zeros of the closed loop transfer function

control performance of the controlled output

associated control input with and without saturation generated by the tuned controller

Also the new window with various calculated quality criteria. The background color indicates the relative property of the value. The green background color indicates suitable value, the yellow color medium, and the red color is used for relatively high value. These color-based decisions have just informative significance.

Quality Criteria

Output parameters:

Settling_Time - settling time

Max_Overshoot - maximal overshoot [%]

IAE

ISE

ITAE

ITSE

ISTAE

ISTSE

ISE_u

ISE_du

ISE_de

Using the button [Back] the previous window will be returned.

Software Settings

In the main window of the software, you can press the [Setup] button, which opens a new window. It contains 4 options:

[Shut Down] – properly shut down the program and saved some settings, such as the language preferences or color effects.

[Reset] - restart the program PIDDESIGN.

[Close Graphs] - close all windows with depicted graphs, which can be used when longer work with the program is necessary.

[Help] – runs file „help.html“.

Illustrative Examples

Example 1.1

PID controller tuning for controlled system described by the known transfer function

Using the button [Controller Tuning] of the main window, the new window for controlled system parameters design will be opened. The aperiodic process can be described using transfer function by Strejc (1). The damped periodic process can be described using the associated parameters of the transfer function (2).

G = K/(Ts + 1)^nexp( - D*s) (1)

G_pe = K/(T_pe^2s + 2ksi_peT_pes + 1)exp( - D_pes) (2)

Inputs of the transfer function by Strejc:

n - order

K - gain

T - time constant

D - time delay

Inputs of the damped periodic transfer function:

K - gain

T_pe - time constant

ksi_pe - damping coefficient - values from [0;1]

D_pe - time delay

Using the button [Controller Tuning] opens the new window for PID controller tuning.
The required type of the PID controller can be chosen using the associated radio-button:

P

PI

PID

PD

and choosing the radio-button of the required class of controller tuning methods:

Experimental methods

Analytical methods

Using the popup menu enables to choose from the list of the available methods.

Using the button [Controller tuning] the controller with the set properties will be designed.
A new window for control performance check using the simulation of control will be opened.
In the upper left part of the window, the calculated parameters of the designed controller (3) are shown.

Gr = (Z_Rs + Z_R/T_I + Z_RT_D*s^2)/s (3)

PID Controller Parameters

Input & Output parameters:

Z_R - proportional gain

T_I - integral time constant

T_D - derivative time constant

T_R - antiwindup parameter of an integral part

T_D - filter of the derivative part

In the upper right part are shown the parameters of the controlled system (4).

G = NUM/DENexp( - Ds) (4)

Process Model

Input & Output parameters:

NUM - numerator of the controlled system transfer function

DEN - denominator of the controlled system transfer function

D - time delay of the controlled system

In the middle left part of are shown the parameters for the setpoint tracking.

Setpoint w(t)

Input parameters:

W_Initial - initial value of set point

W_Final - final value of set point

W_Step_Change - time of the step change

In the middle right part of are shown the parameters for the disturbance rejection.

Disturbance r(t)

Input parameters:

R_Initial - initial value of disturbance

R_Final - final value of disturbance

R_Step_Change - time of the step change

In the upper right part are shown

Simulation parameters

Input parameters:

Control_Precision - tolerance of the set point

Sim_Time - simulation time

U_Min_Boundary - lower constraint of the control input

U_Max_Boundary - upper constraint of the control input

Using the button [Step response] the simulation of control will be started.

Then the various figures are opened:

poles and zeros of the closed loop transfer function

control performance of the controlled output

associated control input generated by the tuned controller

And the new window with various calculated quality criteria. The background color indicates the relative property of the value. The green background color indicates suitable value, the yellow color medium, and the red color is used for relatively high value. These color-based decisions have just informative significance.